our @common_letters = ();
    our @wordsCopy = @words;
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should be

    local our @common_letters;
    local our @wordsCopy = @words;
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Calling subroutines is expensive. I'd try replacing

    local our @common_letters;
    local our @wordsCopy = @words;
    my $reference = shift @wordsCopy;

    $reference =~ /(.)(?{        
       ...
    })/gx;
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with

    my @common_letters;
    my @wordsCopy = @words;
    my $reference = shift @wordsCopy;

    while ($reference =~ /(.)/g) {
       ...
    }
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There's also

    for my $c($reference =~ /./g)  # uses $c instead of $1
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and

    for my $c (split(//, $reference))  # uses $c instead of $1
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The "() =" is useless.

What's with the use of $bolean? Aside from the fact that it should be spelled "boolean",

       my $bolean = 1; 
       for ( @wordsCopy ) 
       { 
           if ( substr( $_, $position, 1 ) ne $letter )
           { 
               $bolean = 0; 
               last
           } 
       }
       $common_letters[ $position ] = $letter if ( $bolean );
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can be written as

       for ( @wordsCopy ) 
       { 
           if ( substr( $_, $position, 1 ) ne $letter )
           { 
               $common_letters[ $position ] = $letter; 
               last
           } 
       }
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Seems to me

    my @wordsCopy = @words;
    my $reference = shift @wordsCopy;
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is a roundabout way of doing

    my ($reference, @wordsCopy) = @words;
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It might be faster to split the words into arrays at the top of the function then using array lookups instead of substr.

       for ( @splitWord ) 
       { 
           if ( $_->[$position] ne $letter )
           { 
               $bolean = 0;
               last
           } 
       }
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